Time: November 21, 2024, 14:00

Venue: Room 301, Building A5, Institute of Mathematics, VAST

Online participation: Join Zoom Meeting

https://us06web.zoom.us/j/82927090825?pwd=sCz1LoTwwU9lBgM74B7Q1G1jytdD3m.1

Meeting ID: 829 2709 0825

Passcode: 123456

Abstract: The inverse Galois problem asks whether every finite group can be realized as the Galois group of some finite Galois extension of the field Q of rational numbers. This problem is still open, even if many partial results have been obtained. The lectures will present some of these results and a general approach due to Hilbert, via the construction of appropriate Galois extensions of the field of rational functions Q(t). Then we will turn to an analog of the inverse Galois problem for function fields in one variable over an algebraically closed field, where a positive answer is known. Finally, we will discuss a further analog, which asks whether every algebraic group can be realized as the automorphism group of some projective variety. Here the answer is generally negative, as shown by Lombardo and Maffei. But it is positive for linear algebraic groups, due to the work of Florence.